# Package sagbi/SB.Interreduced

From ApCoCoAWiki

This article is about a function from ApCoCoA-2. |

## SB.Interreduced

This function is the same as the CoCoA function `interreduced`, just with Subalgebra reduction instead of Gröbner reduction.

### Syntax

SB.Interreduced(L: LIST of POLY): LIST of POLY

### Description

This function takes a list `L` and returns a list `L'` such that `K[L] = K[L']`, but `L'` is Subalgebra interreduced, i.e. no term appearing in the support of one of the polynomials in `L` is a product of terms appearing as leading terms of the other polynomials in `L'`.

@param

`L`A list of polynomials@return An interreduced list of polynomials

#### Example

Use QQ[x,y,z], DegRevLex; L := [x^2*z^2 +x*y*z^2 +y^2*z^2, x, x*z, y*z^2]; SB.Interreduced(L); -- [x, x*z, y*z^2, y^2*z^2]

#### Example

Use QQ[x,y,z], DegRevLex; L := [x +y +z, x*y +x*z +y*z, x*y*z]; SB.Interreduced(L) = L; -- true -- Hence L is a SAGBI basis of QQ[L]

### See also

Package sagbi/SB.ReductionStep